Deriving Capitalization Rates

Deriving Capitalization Rates

This chapter delves into the scientific principles and practical methods behind deriving capitalization rates (cap rates), a critical component of the direct capitalization approach to real estate valuation. We will explore various techniques, their underlying assumptions, and their applicability in different market scenarios.

1. Introduction to Capitalization Rates

A capitalization rate (Ro) is a ratio that expresses the relationship between a property’s net operating income (NOI) and its value (V). It represents the rate of return an investor can expect to receive on their investment, assuming the property is purchased with cash. Mathematically, it is expressed as:

• Equation 1: Basic Cap Rate Formula

  Ro = NOI / V

The cap rate is influenced by several factors, including:

• Risk: Higher-risk properties typically have higher cap rates to compensate investors for the increased uncertainty.
• Growth Expectations: Properties with higher expected income growth often have lower cap rates because investors are willing to pay more for future income potential.
• Market Conditions: Supply and demand dynamics, interest rates, and overall economic conditions can all impact cap rates.
• Property Type and Location: Different property types and locations exhibit varying risk profiles and growth expectations, leading to diverse cap rates.

2. Direct Extraction from Comparable Sales

The most straightforward method for deriving a cap rate is through direct extraction from comparable sales data. This involves analyzing recent transactions of similar properties in the same market to identify the relationship between their NOI and sale price.

• Procedure:

  1. Identify Comparable Sales: Gather data on recent sales of properties that are similar to the subject property in terms of location, size, age, property type, and income-generating potential.
  2. Determine NOI: For each comparable sale, accurately determine the Net Operating Income (NOI) for the year following the sale. This requires careful analysis of income and expense statements.
  3. Calculate Cap Rates: Divide the NOI of each comparable property by its sale price to calculate its cap rate using Equation 1 (Ro = NOI / V).
  4. Reconcile and Select a Cap Rate: Analyze the range of cap rates derived from the comparable sales and reconcile any differences based on the relative strengths and weaknesses of each comparable. Factors to consider include differences in location, physical condition, lease terms, and overall market conditions.

• Example:

  Assume three comparable properties have the following data:

  Property	Sale Price (V)	NOI	Cap Rate (Ro = NOI/V)
  Comp 1	$1,000,000	$80,000	8.0%
  Comp 2	$1,100,000	$93,500	8.5%
  Comp 3	$950,000	$71,250	7.5%

  Based on this data, an appraiser might select a cap rate of 8.0% for the subject property, considering the similarities and differences between the comparables.

• Limitations:

  • The accuracy of this method relies heavily on the availability of reliable sales data and accurate NOI information.
  • Differences in the future income potential of the comparables relative to the subject property can skew the extracted cap rates. For example, if the subject property has greater upside potential due to rent growth, the extracted cap rate may be too high.
  • Finding truly comparable properties with similar income patterns and risk profiles can be challenging, particularly in less active markets.

3. Utilizing the Effective Gross Income Multiplier (EGIM) and Net Income Ratio (NIR)

If market data on EGIM and NIR is available, an alternative approach to derive capitalization rates uses the following formula:

• Equation 2: Cap Rate Derivation from EGIM and NIR

  Ro = NIR / EGIM

Where:

• NIR = Net Income Ratio (NOI / Effective Gross Income)
• EGIM = Effective Gross Income Multiplier (Sale Price / Effective Gross Income)

This method can be useful when detailed income and expense data for comparable sales is limited, but information on EGIM and NIR is readily available.

• Example:

  A property has an EGIM of 5.5 and an expense ratio of 52%. The NIR is calculated as:

  NIR = 1 - Expense Ratio = 1 - 0.52 = 0.48

  Therefore, the capitalization rate is:

  Ro = 0.48 / 5.5 = 0.0873 or 8.73%

• Limitations:

  • This method relies on the accuracy and relevance of the EGIM and NIR data.
  • It assumes a stable relationship between effective gross income and net operating income, which may not always hold true.

4. Band of Investment Techniques

Band of investment techniques partition the overall capitalization rate into components based on the different sources of capital used to finance the property. This approach considers the perspective of both the lender (mortgage) and the equity investor.

4.1 Mortgage and Equity Components

This method breaks down the cap rate into weighted mortgage and equity components. The weights represent the proportion of debt and equity financing used in the transaction.

• Equation 3: Band of Investment (Mortgage and Equity)

  Ro = (M x Rm) + ((1 - M) x Re)

Where:

• M = Loan-to-Value Ratio (LTV)
• Rm = Mortgage Constant (Annual Debt Service / Loan Amount)
• Re = Equity Capitalization Rate (Equity Dividend / Equity Investment)

The mortgage constant (Rm) represents the annual debt service as a percentage of the loan amount. It can be calculated using a financial calculator or a mortgage amortization formula. The equity capitalization rate (Re) represents the rate of return required by the equity investor.

• Example:

  A property is financed with a 75% loan-to-value ratio (M = 0.75). The mortgage has an annual interest rate of 10% with monthly payments over 25 years, resulting in a mortgage constant of 0.10904 (Rm = 0.10904). The equity investor requires a 13% return (Re = 0.13). The overall capitalization rate is:

  Ro = (0.75 x 0.10904) + (0.25 x 0.13) = 0.08178 + 0.0325 = 0.11428 or 11.43%

• Derivation of Mortgage Constant (Rm):

  The mortgage constant, RM, can be calculated by dividing the annual debt service (ADS) by the initial amount of the mortgage.

  It can also be calculated on a financial calculator as follows:

  25 g n Number of Years (25)
  10 g i Interest Rate (10%)
  1 $ Present Value (1.000000)
  0 M Future Value (0.000000)
  P Solve for PMT (0.009087)
  RM = PMT × 12:

  Multiply the result (PMT) by 12.

  RM = PMT x 12 => 0.009087 x 12 = 0.10904

• Limitations:

  • Estimating the equity capitalization rate (Re) can be subjective, as it reflects the investor’s individual risk preferences and return expectations.
  • This method assumes that the mortgage and equity components are independent, which may not always be the case.
  • The equity capitalization rate can vary, even to a negative number in some cases.

4.2 Land and Building Components

This method is less common. It allocates the overall cap rate to the land and building components of the property. It requires knowledge of the land-to-building ratio, land capitalization rate (Rl), and building capitalization rate (Rb).

• Equation 4: Band of Investment (Land and Building)

  Ro = (Land Ratio x Rl) + (Building Ratio x Rb)

• Example:

  A property has a 25:75 land-to-building ratio. The land capitalization rate is 9% (Rl = 0.09), and the building capitalization rate is 13% (Rb = 0.13). The overall capitalization rate is:

  Ro = (0.25 x 0.09) + (0.75 x 0.13) = 0.0225 + 0.0975 = 0.12 or 12%

• Limitations:

  • This method is highly theoretical because buyers and sellers do not directly transfer separate rights for land and buildings. They only transfer the rights in realty.
  • Determining separate capitalization rates for land and building can be challenging.

5. Debt Coverage Ratio (DCR) Formula (Mortgage Underwriter’s Method)

This method, also known as the mortgage underwriter’s method, leverages data obtained directly from mortgage lenders to derive the overall cap rate. It directly considers the terms available in the mortgage market.

• Equation 5: Cap Rate Derivation from DCR

  Ro = M x Rm x DCR

Where:

• DCR = Debt Coverage Ratio (NOI / Annual Debt Service)
• M = Loan-to-Value Ratio
• Rm = Mortgage Constant

This method provides a market-oriented approach, as most real estate transactions involve mortgage financing.

• Example:

  A property has an estimated NOI of $100,000. The lender offers a 75% loan-to-value ratio with a 9% annual interest rate and full amortization over 20 years, subject to a debt coverage ratio of 1.2. The annual mortgage constant for a 20-year loan at 9% is 0.10797. The overall capitalization rate is:

  Ro = 0.75 x 0.10797 x 1.2 = 0.09717 or 9.72%

  The mortgage constant, RM, can be calculated on a financial calculator as follows:

  9 g i Interest Rate (9%)
  20 g n Number of Years (20)
  1 $ Present Value (1.000000)
  0 M Future Value (0.000000)
  Solve for P = 0.008997

  Multiply the result (PMT) by 12.

  RM = PMT x 12 => 0.008997 x 12 = 0.107967

• Limitations:

  • This method relies heavily on the lender’s willingness to provide financing and the terms they offer.
  • Lenders may be reluctant to finance certain types of properties, which can affect the accuracy of the cap rate estimate.
  • Debt coverage ratios can vary depending on individual banks.
  • The equity investor’s perspective is not directly considered in the DCR formula.

6. Market Surveys

Appraisers often use capitalization rates reported by real estate research firms and market surveys as supporting evidence for their own cap rate estimates. These surveys provide a broad picture of market trends and investor expectations. Talking with real estate brokers about the capitalization rates they see in sales of income-producing property in a specific market is also a common source of information used by appraisers.

• Considerations:

  • Evaluate the source of the survey data and the methodology used to derive the reported cap rates.
  • Assess the relevance of national or regional data to the local real estate market.
  • Use survey data as a general guideline, but always rely on your own analysis of comparable sales and market conditions.

7. Residual Techniques

Residual techniques are used to estimate the value of a property when certain components of the income stream or value are known. These techniques are applicable to cases where, for example, net income, land value, and land and building capitalization rates are available.

(Note: The PDF extract does not include the actual formulas, beyond mentioning the “residual techniques” name. If you can find PDFs that list them, let me know.)

8. Conclusion

Deriving accurate and reliable capitalization rates is crucial for effective real estate valuation using the direct capitalization approach. By understanding the scientific principles behind cap rates and applying the various techniques discussed in this chapter, appraisers can develop well-supported value conclusions that reflect the unique characteristics of the property and the prevailing market conditions. Careful consideration of the limitations of each method and the reconciliation of multiple indicators are essential for ensuring the accuracy and credibility of the valuation.